(p+1)(p+5)=0

Solution for (p+1)(p+5)=0 equation:

Simplifying
(p + 1)(p + 5) = 0

Reorder the terms:
(1 + p)(p + 5) = 0

Reorder the terms:
(1 + p)(5 + p) = 0

Multiply (1 + p) * (5 + p)
(1(5 + p) + p(5 + p)) = 0
((5 * 1 + p * 1) + p(5 + p)) = 0
((5 + 1p) + p(5 + p)) = 0
(5 + 1p + (5 * p + p * p)) = 0
(5 + 1p + (5p + p2)) = 0

Combine like terms: 1p + 5p = 6p
(5 + 6p + p2) = 0

Solving
5 + 6p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(5 + p)(1 + p) = 0

Subproblem 1
Set the factor '(5 + p)' equal to zero and attempt to solve:

Simplifying
5 + p = 0

Solving
5 + p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + p = 0 + -5
p = 0 + -5

Combine like terms: 0 + -5 = -5
p = -5

Simplifying
p = -5
Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve:

Simplifying
1 + p = 0

Solving
1 + p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + p = 0 + -1
p = 0 + -1

Combine like terms: 0 + -1 = -1
p = -1

Simplifying
p = -1
Solution
p = {-5, -1}